Transmuted Exponentiated Inverse Weibull Distribution with Applications in Medical Sciences

Uzma Jan; Kawsar Fatima; S.P Ahmad

doi:https://doi.org/10.14445/22315373/IJMTT-V50P526

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 50 | Number 3 | Year 2017 | Article Id. IJMTT-V50P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P526

Transmuted Exponentiated Inverse Weibull Distribution with Applications in Medical Sciences

Uzma Jan, Kawsar Fatima, S.P Ahmad

Citation :

Uzma Jan, Kawsar Fatima, S.P Ahmad, "Transmuted Exponentiated Inverse Weibull Distribution with Applications in Medical Sciences," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 3, pp. 160-167, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P526

Abstract

This manuscript considers the transmuted model of the Exponentiated Inverse Weibull distribution. A comprehensive description of the mathematical properties of the proposed model is given in this article. The various properties which include reliability analysis, moments, quantile function, median, moment generating function, characteristic function and order statistics have been discussed in the paper. The method of maximum likelihood estimation has been used for estimating the parameters of the newly proposed distribution. The usefulness of the newly developed model over its sub models for better fitting is illustrated both by the simulated as well as real life data sets.

Keywords

Transmuted Exponentiated Inverse, Weibull Distribution, Reliability analysis, Moments, Quantile function, Order Statistics, AIC, HQIC.

References

[1] A. Ahmad, S.P. Ahmad, and A. Ahmed, “Transmuted Inverse Rayleigh Distribution: A Generalization of the Inverse Rayleigh Distribution,” Mathematical Theory and Modeling, Vol. 4, No. 7, pp. 90-9, 2014.
[2] A. Flaih, H. Elsalloukh, E. Mendi, M. Milanova, “The exponentiated inverted Weibull distribution,” Appl. Math. Inf. Sci., Vol.6, No.2, pp.167-171, 2012.
[3] A. Renyi, “On Measures of Information and Entropy”, Proc. of the Fourth Berk. Sym. on Maths, Stats and Prob., 1960,pp. 547-561.
[4] A.Z. Keller, A.R.R. Kamath and U.D. Perera, “Reliability analysis of CNC machine tools,” Relia.Engg, Vol. 3, No.6, pp. 449–473, 1982.
[5] Drapella, “Complementary Weibull distribution: unknown or just forgotten,” Qual. Relia.. Engg. Inter., Vol. 9, pp. 383– 385.
[6] E. K. AL Hussaini, “On exponentiated class of distributions,” J. Stat. Th and Appl. Vol. 8, pp. 41-63, 2010. [7] E. T. Lee and J. W. Wang, “Statistical methods for survival data analysis”, 3rd ed., John Wiley and Sons, New York, USA, 2003.
[8] G.S. Mudholkar, D.K. Srivastava and M. Freimer, “The exponentiated Weibull family: a reanalysis of the bus-motor failure data,” Technometrics, Vol. 37, pp.436-445, 1995.
[9] J. Havrda and F. Charvát, “Quantification Method of Classification Processes, Concept of Structural –Entropy,” Kybernetika, Vol. 3, pp. 30-35, 1967.
[10] K. Ahmad, S.P. Ahmad, and A. Ahmed, “Structural properties of transmuted Weibull distribution,” JMASM, Vo1.4, No.2, pp.140-158, 2015.
[11] M. Aleem and G.R. Pasha, “Ratio, product and single moments of order statistics from inverse Weibull distribution”. Journal of Statistics, Vol.10, No. 1, pp.1–7, 2003.
[12] M.N. Nassar and F. H. Eissa, “On exponentiated Weibull distribution,” Commun. Statist. Th.Meth. Vol.32, pp. 1317- 1336, 2003.
[13] M.W.A. Ramos, G.M. Cordeiro, P.R.D. Marinho, C.R.B. Dais, G.G. Hamedani, “The Zografos Balakrishan log logistic distribution: properties and applications.” J. Stat. Th and Appl, Vol.12, pp. 225-244, 2013.
[14] R. D. Gupta and D. Kundu, “Exponentiated exponential family: an alternative to gamma and Weibull distributions,” Biometrical Journal, Vol. 43, pp.117-130, (2001).
[15] S. K. Ashour, M. A. Eltehiwy, “Transmuted Lomax Distribution,” Amer. J. Appl. Math. Stat. Vol. 1, No. 6, pp.121-127, 2013.
[16] Shaw, W. and I. Buckley. “The Alchemy of Probability Distributions: Beyond Gram-Charlier Expansions, and a Skew-Kurtotic-Normal Distribution from a Rank Transmutation Map,” Res. Rep. 2009.